Restore GPU-backed UInt128 pow2 Montgomery helper
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Marek Lemańczyk committed
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commit
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11 files changed
+1561
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@@ -0,0 +1,269 @@
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using System;
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using System.Numerics;
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using System.Runtime.CompilerServices;
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namespace PerfectNumbers.Core.Gpu;
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public struct GpuRational : IEquatable<GpuRational>, IComparable<GpuRational>
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{
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private const double Pow64 = 18446744073709551616.0;
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public GpuUInt128 Numerator;
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public GpuUInt128 Denominator;
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public static readonly GpuRational Zero = new(GpuUInt128.Zero, GpuUInt128.One);
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public static readonly GpuRational One = new(GpuUInt128.One, GpuUInt128.One);
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public GpuRational(GpuUInt128 numerator)
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: this(numerator, GpuUInt128.One)
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{
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public GpuRational(ulong numerator)
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: this(new GpuUInt128(numerator), GpuUInt128.One)
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{
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public GpuRational(GpuUInt128 numerator, GpuUInt128 denominator)
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{
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if (denominator.IsZero)
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{
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throw new DivideByZeroException("GpuRational denominator cannot be zero.");
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}
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Numerator = numerator;
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Denominator = denominator;
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Normalize();
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public GpuRational(ulong numerator, ulong denominator)
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: this(new GpuUInt128(numerator), new GpuUInt128(denominator))
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{
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}
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public readonly bool IsZero
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{
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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get => Numerator.IsZero;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static implicit operator GpuRational(GpuUInt128 value) => new(value);
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static implicit operator GpuRational(ulong value) => new(value);
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public void Add(in GpuRational other)
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{
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GpuUInt128 leftDenominator = Denominator;
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GpuUInt128 rightDenominator = other.Denominator;
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GpuUInt128 gcd = GpuUInt128.BinaryGcd(leftDenominator, rightDenominator);
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if (gcd != GpuUInt128.One)
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{
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leftDenominator = GpuUInt128.DivideExact(leftDenominator, gcd);
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rightDenominator = GpuUInt128.DivideExact(rightDenominator, gcd);
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// Reusing both denominator variables to store their reduced values because the unreduced inputs are no longer needed.
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}
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Numerator.Mul(rightDenominator);
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GpuUInt128 scaledOtherNumerator = other.Numerator;
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scaledOtherNumerator.Mul(leftDenominator);
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Numerator.Add(scaledOtherNumerator);
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Denominator = leftDenominator;
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// Denominator now holds the reduced left denominator; multiply by the original right denominator to form the LCM.
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Denominator.Mul(other.Denominator);
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Normalize();
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public void Sub(in GpuRational other)
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{
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GpuUInt128 leftDenominator = Denominator;
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GpuUInt128 rightDenominator = other.Denominator;
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GpuUInt128 gcd = GpuUInt128.BinaryGcd(leftDenominator, rightDenominator);
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if (gcd != GpuUInt128.One)
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{
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leftDenominator = GpuUInt128.DivideExact(leftDenominator, gcd);
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rightDenominator = GpuUInt128.DivideExact(rightDenominator, gcd);
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// Reusing the denominator variables to keep the reduced values since the raw denominators are no longer required.
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}
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Numerator.Mul(rightDenominator);
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GpuUInt128 scaledOtherNumerator = other.Numerator;
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scaledOtherNumerator.Mul(leftDenominator);
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if (Numerator.CompareTo(scaledOtherNumerator) < 0)
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{
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throw new InvalidOperationException("Resulting GpuRational would be negative.");
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}
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Numerator.Sub(scaledOtherNumerator);
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Denominator = leftDenominator;
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Denominator.Mul(other.Denominator);
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Normalize();
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public void Mul(in GpuRational other)
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{
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GpuUInt128 rightDenominator = other.Denominator;
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GpuUInt128 gcd = GpuUInt128.BinaryGcd(Numerator, rightDenominator);
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if (gcd != GpuUInt128.One)
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{
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Numerator = GpuUInt128.DivideExact(Numerator, gcd);
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rightDenominator = GpuUInt128.DivideExact(rightDenominator, gcd);
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// Reusing rightDenominator to keep the reduced value because the original denominator is no longer required.
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}
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GpuUInt128 rightNumerator = other.Numerator;
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GpuUInt128 leftDenominator = Denominator;
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gcd = GpuUInt128.BinaryGcd(rightNumerator, leftDenominator);
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if (gcd != GpuUInt128.One)
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{
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rightNumerator = GpuUInt128.DivideExact(rightNumerator, gcd);
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leftDenominator = GpuUInt128.DivideExact(leftDenominator, gcd);
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// Reusing rightNumerator and leftDenominator after cross-cancellation keeps the intermediates compact.
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}
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Numerator.Mul(rightNumerator);
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Denominator = leftDenominator;
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Denominator.Mul(rightDenominator);
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Normalize();
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public void Div(in GpuRational other)
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{
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if (other.Numerator.IsZero)
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{
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throw new DivideByZeroException("Cannot divide by a zero GpuRational.");
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}
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GpuUInt128 rightNumerator = other.Numerator;
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GpuUInt128 gcd = GpuUInt128.BinaryGcd(Numerator, rightNumerator);
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if (gcd != GpuUInt128.One)
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{
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Numerator = GpuUInt128.DivideExact(Numerator, gcd);
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rightNumerator = GpuUInt128.DivideExact(rightNumerator, gcd);
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// Reusing rightNumerator to store the reduced numerator keeps temporary allocations out of the hot path.
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}
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GpuUInt128 rightDenominator = other.Denominator;
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GpuUInt128 leftDenominator = Denominator;
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gcd = GpuUInt128.BinaryGcd(rightDenominator, leftDenominator);
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if (gcd != GpuUInt128.One)
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{
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rightDenominator = GpuUInt128.DivideExact(rightDenominator, gcd);
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leftDenominator = GpuUInt128.DivideExact(leftDenominator, gcd);
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// Reusing both denominator variables here mirrors the cross-cancellation performed on the numerators.
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}
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Numerator.Mul(rightDenominator);
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Denominator = leftDenominator;
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Denominator.Mul(rightNumerator);
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Normalize();
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static GpuRational operator +(GpuRational left, GpuRational right)
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{
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left.Add(right);
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return left;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static GpuRational operator -(GpuRational left, GpuRational right)
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{
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left.Sub(right);
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return left;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static GpuRational operator *(GpuRational left, GpuRational right)
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{
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left.Mul(right);
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return left;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static GpuRational operator /(GpuRational left, GpuRational right)
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{
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left.Div(right);
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return left;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public readonly int CompareTo(GpuRational other)
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{
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GpuUInt128 leftScaled = Numerator;
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leftScaled.Mul(other.Denominator);
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GpuUInt128 rightScaled = other.Numerator;
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rightScaled.Mul(Denominator);
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return leftScaled.CompareTo(rightScaled);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public readonly bool Equals(GpuRational other) => Numerator == other.Numerator && Denominator == other.Denominator;
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public override readonly bool Equals(object? obj) => obj is GpuRational other && Equals(other);
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public override readonly int GetHashCode() => HashCode.Combine(Numerator, Denominator);
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static bool operator ==(GpuRational left, GpuRational right) => left.Equals(right);
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static bool operator !=(GpuRational left, GpuRational right) => !left.Equals(right);
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static bool operator <(GpuRational left, GpuRational right) => left.CompareTo(right) < 0;
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static bool operator >(GpuRational left, GpuRational right) => left.CompareTo(right) > 0;
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static bool operator <=(GpuRational left, GpuRational right) => left.CompareTo(right) <= 0;
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static bool operator >=(GpuRational left, GpuRational right) => left.CompareTo(right) >= 0;
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public readonly double ToDouble()
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{
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double numerator = Numerator.High == 0UL ? Numerator.Low : Numerator.High * Pow64 + Numerator.Low;
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double denominator = Denominator.High == 0UL ? Denominator.Low : Denominator.High * Pow64 + Denominator.Low;
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return numerator / denominator;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public override readonly string ToString() => $"{Numerator}/{Denominator}";
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private void Normalize()
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{
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if (Numerator.IsZero)
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{
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Denominator = GpuUInt128.One;
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return;
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}
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GpuUInt128 gcd = GpuUInt128.BinaryGcd(Numerator, Denominator);
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if (gcd != GpuUInt128.One)
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{
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Numerator = GpuUInt128.DivideExact(Numerator, gcd);
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Denominator = GpuUInt128.DivideExact(Denominator, gcd);
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}
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}
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}
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@@ -54,6 +54,26 @@ public struct GpuUInt128 : IComparable<GpuUInt128>, IEquatable<GpuUInt128>
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get => High == 0UL && Low == 0UL;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public readonly int GetBitLength()
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{
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if (High != 0UL)
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{
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return 64 + (64 - BitOperations.LeadingZeroCount(High));
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}
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ulong low = Low;
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if (low == 0UL)
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{
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return 0;
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}
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return 64 - BitOperations.LeadingZeroCount(low);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static int GetBitLength(GpuUInt128 value) => value.GetBitLength();
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static implicit operator GpuUInt128(UInt128 value) => new(value);
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@@ -564,6 +584,43 @@ public struct GpuUInt128 : IComparable<GpuUInt128>, IEquatable<GpuUInt128>
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Low = lowPart;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static GpuUInt128 DivideExact(GpuUInt128 dividend, GpuUInt128 divisor)
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{
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int divisorBits = divisor.GetBitLength();
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int shift = dividend.GetBitLength() - divisorBits;
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GpuUInt128 quotient = Zero;
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GpuUInt128 remainder = dividend;
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GpuUInt128 shiftedDivisor = divisor << shift;
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GpuUInt128 quotientBit = One << shift;
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while (true)
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{
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if (remainder.CompareTo(shiftedDivisor) >= 0)
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{
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remainder.Sub(shiftedDivisor);
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quotient.Add(quotientBit);
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}
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if (shift == 0)
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{
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break;
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}
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shift--;
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shiftedDivisor.ShiftRight(1);
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quotientBit.ShiftRight(1);
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}
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if (!remainder.IsZero)
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{
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throw new InvalidOperationException("DivideExact requires divisible operands.");
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}
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return quotient;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public void Xor(GpuUInt128 other)
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{
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@@ -1,9 +1,12 @@
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using System;
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using System.Buffers;
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using System.Collections.Concurrent;
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using ILGPU;
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using ILGPU.Runtime;
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using System.Numerics;
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using PerfectNumbers.Core;
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using System.Runtime.InteropServices;
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using System.Runtime.CompilerServices;
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namespace PerfectNumbers.Core.Gpu;
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internal enum GpuPow2ModStatus
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@@ -16,10 +19,24 @@ internal enum GpuPow2ModStatus
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internal static class PrimeOrderGpuHeuristics
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{
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private static readonly ConcurrentDictionary<ulong, byte> OverflowedPrimes = new();
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private static readonly ConcurrentDictionary<UInt128, byte> OverflowedPrimesWide = new();
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private static readonly ConcurrentDictionary<Accelerator, Action<AcceleratorStream, Index1D, ArrayView1D<ulong, Stride1D.Dense>, MontgomeryDivisorData, ArrayView1D<ulong, Stride1D.Dense>>> Pow2ModKernelCache = new();
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private static readonly ConcurrentDictionary<Accelerator, Action<AcceleratorStream, Index1D, ArrayView1D<GpuUInt128, Stride1D.Dense>, GpuUInt128, ArrayView1D<GpuUInt128, Stride1D.Dense>>> Pow2ModKernelWideCache = new();
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private const int WideStackThreshold = 8;
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private static PrimeOrderGpuCapability s_capability = PrimeOrderGpuCapability.Default;
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private const int Pow2WindowSizeBits = 8;
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private const int Pow2WindowOddPowerCount = 1 << (Pow2WindowSizeBits - 1);
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private const ulong Pow2WindowFallbackThreshold = 32UL;
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[InlineArray(Pow2WindowOddPowerCount)]
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private struct Pow2OddPowerTable
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{
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private GpuUInt128 _element0;
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}
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internal static ConcurrentDictionary<ulong, byte> OverflowRegistry => OverflowedPrimes;
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internal static ConcurrentDictionary<UInt128, byte> OverflowRegistryWide => OverflowedPrimesWide;
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internal static void OverrideCapabilitiesForTesting(PrimeOrderGpuCapability capability)
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{
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@@ -89,6 +106,59 @@ internal static class PrimeOrderGpuHeuristics
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return computed ? GpuPow2ModStatus.Success : GpuPow2ModStatus.Unavailable;
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}
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public static GpuPow2ModStatus TryPow2Mod(UInt128 exponent, UInt128 prime, out UInt128 remainder)
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{
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Span<UInt128> exponents = stackalloc UInt128[1];
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Span<UInt128> remainders = stackalloc UInt128[1];
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exponents[0] = exponent;
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GpuPow2ModStatus status = TryPow2ModBatch(exponents, prime, remainders);
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remainder = remainders[0];
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return status;
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}
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public static GpuPow2ModStatus TryPow2ModBatch(ReadOnlySpan<UInt128> exponents, UInt128 prime, Span<UInt128> remainders)
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{
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if (exponents.Length == 0)
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{
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return GpuPow2ModStatus.Success;
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}
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if (remainders.Length < exponents.Length)
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{
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throw new ArgumentException("Remainder span is shorter than the exponent span.", nameof(remainders));
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}
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Span<UInt128> target = remainders.Slice(0, exponents.Length);
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target.Clear();
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ConcurrentDictionary<UInt128, byte> overflowRegistryWide = OverflowedPrimesWide;
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if (overflowRegistryWide.ContainsKey(prime))
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{
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return GpuPow2ModStatus.Overflow;
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}
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PrimeOrderGpuCapability capability = s_capability;
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if (prime.GetBitLength() > capability.ModulusBits)
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{
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overflowRegistryWide[prime] = 0;
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return GpuPow2ModStatus.Overflow;
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}
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for (int i = 0; i < exponents.Length; i++)
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{
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if (exponents[i].GetBitLength() > capability.ExponentBits)
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{
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return GpuPow2ModStatus.Overflow;
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}
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}
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bool computed = TryComputeOnGpuWide(exponents, prime, target);
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return computed ? GpuPow2ModStatus.Success : GpuPow2ModStatus.Unavailable;
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}
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private static bool TryComputeOnGpu(ReadOnlySpan<ulong> exponents, ulong prime, Span<ulong> results)
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{
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try
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@@ -128,12 +198,94 @@ internal static class PrimeOrderGpuHeuristics
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private static void ComputePow2ModCpu(ReadOnlySpan<ulong> exponents, ulong prime, Span<ulong> results)
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{
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for (int i = 0; i < exponents.Length; i++)
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int length = exponents.Length;
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for (int i = 0; i < length; i++)
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{
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results[i] = Pow2ModCpu(exponents[i], prime);
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}
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}
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private static bool TryComputeOnGpuWide(ReadOnlySpan<UInt128> exponents, UInt128 prime, Span<UInt128> results)
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{
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int length = exponents.Length;
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if (length == 0)
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{
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return true;
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}
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GpuUInt128[]? rentedExponents = null;
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GpuUInt128[]? rentedResults = null;
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var lease = GpuKernelPool.GetKernel(useGpuOrder: true);
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try
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||||
{
|
||||
using var execution = lease.EnterExecutionScope();
|
||||
Accelerator accelerator = lease.Accelerator;
|
||||
AcceleratorStream stream = lease.Stream;
|
||||
var kernel = GetPow2ModWideKernel(accelerator);
|
||||
using var exponentBuffer = accelerator.Allocate1D<GpuUInt128>(length);
|
||||
using var remainderBuffer = accelerator.Allocate1D<GpuUInt128>(length);
|
||||
|
||||
Span<GpuUInt128> exponentSpan = length <= WideStackThreshold
|
||||
? stackalloc GpuUInt128[length]
|
||||
: new Span<GpuUInt128>(rentedExponents = ArrayPool<GpuUInt128>.Shared.Rent(length), 0, length);
|
||||
|
||||
for (int i = 0; i < length; i++)
|
||||
{
|
||||
exponentSpan[i] = (GpuUInt128)exponents[i];
|
||||
}
|
||||
|
||||
exponentBuffer.View.CopyFromCPU(ref MemoryMarshal.GetReference(exponentSpan), length);
|
||||
remainderBuffer.MemSetToZero();
|
||||
|
||||
GpuUInt128 modulus = (GpuUInt128)prime;
|
||||
kernel(stream, length, exponentBuffer.View, modulus, remainderBuffer.View);
|
||||
|
||||
stream.Synchronize();
|
||||
|
||||
Span<GpuUInt128> resultSpan = length <= WideStackThreshold
|
||||
? stackalloc GpuUInt128[length]
|
||||
: new Span<GpuUInt128>(rentedResults = ArrayPool<GpuUInt128>.Shared.Rent(length), 0, length);
|
||||
|
||||
remainderBuffer.View.CopyToCPU(ref MemoryMarshal.GetReference(resultSpan), length);
|
||||
|
||||
for (int i = 0; i < length; i++)
|
||||
{
|
||||
results[i] = (UInt128)resultSpan[i];
|
||||
}
|
||||
|
||||
return true;
|
||||
}
|
||||
catch (Exception ex) when (ex is AcceleratorException or InternalCompilerException or NotSupportedException or InvalidOperationException or AggregateException)
|
||||
{
|
||||
ComputePow2ModCpuWide(exponents, prime, results);
|
||||
return true;
|
||||
}
|
||||
finally
|
||||
{
|
||||
if (rentedExponents is not null)
|
||||
{
|
||||
ArrayPool<GpuUInt128>.Shared.Return(rentedExponents, clearArray: false);
|
||||
}
|
||||
|
||||
if (rentedResults is not null)
|
||||
{
|
||||
ArrayPool<GpuUInt128>.Shared.Return(rentedResults, clearArray: false);
|
||||
}
|
||||
|
||||
lease.Dispose();
|
||||
}
|
||||
}
|
||||
|
||||
private static void ComputePow2ModCpuWide(ReadOnlySpan<UInt128> exponents, UInt128 prime, Span<UInt128> results)
|
||||
{
|
||||
int length = exponents.Length;
|
||||
for (int i = 0; i < length; i++)
|
||||
{
|
||||
results[i] = exponents[i].Pow2MontgomeryModWindowed(prime);
|
||||
}
|
||||
}
|
||||
|
||||
private static ulong Pow2ModCpu(ulong exponent, ulong modulus)
|
||||
{
|
||||
if (modulus <= 1UL)
|
||||
@@ -161,8 +313,191 @@ internal static class PrimeOrderGpuHeuristics
|
||||
remainders[index] = exponent.Pow2MontgomeryModWindowed(divisor, keepMontgomery: false);
|
||||
}
|
||||
|
||||
private static Action<AcceleratorStream, Index1D, ArrayView1D<GpuUInt128, Stride1D.Dense>, GpuUInt128, ArrayView1D<GpuUInt128, Stride1D.Dense>> GetPow2ModWideKernel(Accelerator accelerator)
|
||||
{
|
||||
return Pow2ModKernelWideCache.GetOrAdd(accelerator, static accel =>
|
||||
{
|
||||
var loaded = accel.LoadAutoGroupedStreamKernel<Index1D, ArrayView1D<GpuUInt128, Stride1D.Dense>, GpuUInt128, ArrayView1D<GpuUInt128, Stride1D.Dense>>(Pow2ModKernelWide);
|
||||
var kernel = KernelUtil.GetKernel(loaded);
|
||||
return kernel.CreateLauncherDelegate<Action<AcceleratorStream, Index1D, ArrayView1D<GpuUInt128, Stride1D.Dense>, GpuUInt128, ArrayView1D<GpuUInt128, Stride1D.Dense>>>();
|
||||
});
|
||||
}
|
||||
|
||||
private static void Pow2ModKernelWide(Index1D index, ArrayView1D<GpuUInt128, Stride1D.Dense> exponents, GpuUInt128 modulus, ArrayView1D<GpuUInt128, Stride1D.Dense> remainders)
|
||||
{
|
||||
GpuUInt128 exponent = exponents[index];
|
||||
remainders[index] = Pow2ModKernelCore(exponent, modulus);
|
||||
}
|
||||
|
||||
private static GpuUInt128 Pow2ModKernelCore(GpuUInt128 exponent, GpuUInt128 modulus)
|
||||
{
|
||||
if (modulus == GpuUInt128.One)
|
||||
{
|
||||
return GpuUInt128.Zero;
|
||||
}
|
||||
|
||||
if (exponent.IsZero)
|
||||
{
|
||||
return GpuUInt128.One;
|
||||
}
|
||||
|
||||
GpuUInt128 baseValue = new GpuUInt128(2UL);
|
||||
if (baseValue.CompareTo(modulus) >= 0)
|
||||
{
|
||||
baseValue.Sub(modulus);
|
||||
}
|
||||
|
||||
if (ShouldUseSingleBit(exponent))
|
||||
{
|
||||
return Pow2MontgomeryModSingleBit(exponent, modulus, baseValue);
|
||||
}
|
||||
|
||||
int bitLength = exponent.GetBitLength();
|
||||
int windowSize = GetWindowSize(bitLength);
|
||||
int oddPowerCount = 1 << (windowSize - 1);
|
||||
|
||||
Pow2OddPowerTable oddPowers = default;
|
||||
InitializeOddPowers(ref oddPowers, baseValue, modulus, oddPowerCount);
|
||||
|
||||
GpuUInt128 result = GpuUInt128.One;
|
||||
int index = bitLength - 1;
|
||||
|
||||
while (index >= 0)
|
||||
{
|
||||
if (!IsBitSet(exponent, index))
|
||||
{
|
||||
result.MulMod(result, modulus);
|
||||
index--;
|
||||
continue;
|
||||
}
|
||||
|
||||
int windowStart = index - windowSize + 1;
|
||||
if (windowStart < 0)
|
||||
{
|
||||
windowStart = 0;
|
||||
}
|
||||
|
||||
while (!IsBitSet(exponent, windowStart))
|
||||
{
|
||||
windowStart++;
|
||||
}
|
||||
|
||||
int windowBitCount = index - windowStart + 1;
|
||||
for (int square = 0; square < windowBitCount; square++)
|
||||
{
|
||||
result.MulMod(result, modulus);
|
||||
}
|
||||
|
||||
ulong windowValue = ExtractWindowValue(exponent, windowStart, windowBitCount);
|
||||
int tableIndex = (int)((windowValue - 1UL) >> 1);
|
||||
GpuUInt128 factor = oddPowers[tableIndex];
|
||||
result.MulMod(factor, modulus);
|
||||
|
||||
index = windowStart - 1;
|
||||
}
|
||||
|
||||
return result;
|
||||
}
|
||||
|
||||
private static bool ShouldUseSingleBit(in GpuUInt128 exponent) => exponent.High == 0UL && exponent.Low <= Pow2WindowFallbackThreshold;
|
||||
|
||||
private static int GetWindowSize(int bitLength)
|
||||
{
|
||||
if (bitLength <= Pow2WindowSizeBits)
|
||||
{
|
||||
return Math.Max(bitLength, 1);
|
||||
}
|
||||
|
||||
if (bitLength <= 23)
|
||||
{
|
||||
return 4;
|
||||
}
|
||||
|
||||
if (bitLength <= 79)
|
||||
{
|
||||
return 5;
|
||||
}
|
||||
|
||||
if (bitLength <= 239)
|
||||
{
|
||||
return 6;
|
||||
}
|
||||
|
||||
if (bitLength <= 671)
|
||||
{
|
||||
return 7;
|
||||
}
|
||||
|
||||
return Pow2WindowSizeBits;
|
||||
}
|
||||
|
||||
private static void InitializeOddPowers(ref Pow2OddPowerTable oddPowers, GpuUInt128 baseValue, GpuUInt128 modulus, int oddPowerCount)
|
||||
{
|
||||
oddPowers[0] = baseValue;
|
||||
if (oddPowerCount == 1)
|
||||
{
|
||||
return;
|
||||
}
|
||||
|
||||
// Reusing baseValue to hold base^2 for the shared odd-power ladder that follows.
|
||||
baseValue.MulMod(baseValue, modulus);
|
||||
for (int i = 1; i < oddPowerCount; i++)
|
||||
{
|
||||
oddPowers[i] = oddPowers[i - 1];
|
||||
oddPowers[i].MulMod(baseValue, modulus);
|
||||
}
|
||||
}
|
||||
|
||||
private static GpuUInt128 Pow2MontgomeryModSingleBit(GpuUInt128 exponent, GpuUInt128 modulus, GpuUInt128 baseValue)
|
||||
{
|
||||
GpuUInt128 result = GpuUInt128.One;
|
||||
|
||||
while (!exponent.IsZero)
|
||||
{
|
||||
if ((exponent.Low & 1UL) != 0UL)
|
||||
{
|
||||
result.MulMod(baseValue, modulus);
|
||||
}
|
||||
|
||||
exponent.ShiftRight(1);
|
||||
if (exponent.IsZero)
|
||||
{
|
||||
break;
|
||||
}
|
||||
|
||||
// Reusing baseValue to store the squared base for the next iteration.
|
||||
baseValue.MulMod(baseValue, modulus);
|
||||
}
|
||||
|
||||
return result;
|
||||
}
|
||||
|
||||
private static bool IsBitSet(in GpuUInt128 value, int bitIndex)
|
||||
{
|
||||
if (bitIndex >= 64)
|
||||
{
|
||||
return ((value.High >> (bitIndex - 64)) & 1UL) != 0UL;
|
||||
}
|
||||
|
||||
return ((value.Low >> bitIndex) & 1UL) != 0UL;
|
||||
}
|
||||
|
||||
private static ulong ExtractWindowValue(in GpuUInt128 exponent, int windowStart, int windowBitCount)
|
||||
{
|
||||
if (windowStart != 0)
|
||||
{
|
||||
GpuUInt128 shifted = exponent;
|
||||
shifted.ShiftRight(windowStart);
|
||||
ulong mask = (1UL << windowBitCount) - 1UL;
|
||||
return shifted.Low & mask;
|
||||
}
|
||||
|
||||
ulong directMask = (1UL << windowBitCount) - 1UL;
|
||||
return exponent.Low & directMask;
|
||||
}
|
||||
|
||||
internal readonly record struct PrimeOrderGpuCapability(int ModulusBits, int ExponentBits)
|
||||
{
|
||||
public static PrimeOrderGpuCapability Default => new(128, 64);
|
||||
public static PrimeOrderGpuCapability Default => new(128, 128);
|
||||
}
|
||||
}
|
||||
Reference in new issue
Block a user